一类具粘性阻尼项的拟线性波动方程解的局部存在性和整体不存在性（英文）

Local Existence and Global Nonexistence Theorems for a Viscous Damped Quasi-Linear Wave Equations

本文针对三维空间中一类具有粘性阻尼项的拟线性波动方程的初边值问题.利用Galerkin方法和紧性原理,证明了该问题局部解的存在唯一性;借助能量积分不等式证明了该问题的解在有限时间内发生爆破.

In this paper,the existence and uniqueness of the local solution for the initial boundary value problem for a class of three-dimensional space of quasi-linear viscous damping wave equation are proved by the Galerkin method and compactness principle.The blow-up of the solution in limited time for this question is proved by means of the energy integral inequality.